Data-driven simulation of physical systems has recently kindled significant attention, where many neural models have been developed. In particular, mesh-based graph neural networks (GNNs) have demonstrated significant potential in predicting spatiotemporal dynamics across arbitrary geometric domains. However, the existing node-edge message passing mechanism in GNNs limits the model's representation learning ability. In this paper, we proposed a cell-embedded GNN model (aka CeGNN) to learn spatiotemporal dynamics with lifted performance. Specifically, we introduce a learnable cell attribution to the node-edge message passing process, which better captures the spatial dependency of regional features. Such a strategy essentially upgrades the local aggregation scheme from the first order (e.g., from edge to node) to a higher order (e.g., from volume to edge and then to node), which takes advantage of volumetric information in message passing. Meanwhile, a novel feature-enhanced block is designed to further improve the performance of CeGNN and relieve the over-smoothness problem, via treating the latent features as basis functions. The extensive experiments on various PDE systems and one real-world dataset demonstrate that CeGNN achieves superior performance compared with other baseline models, particularly reducing the prediction error with up to 1 orders of magnitude on several PDE systems.

本研究解决了现有图神经网络在节点边缘消息传递机制方面的局限性，提出了一种细胞嵌入的图神经网络模型（CeGNN），能有效捕捉区域特征的空间依赖性。研究结果显示，CeGNN在各种偏微分方程系统上表现优越，预测误差在多个系统中减少了一个数量级，具有显著的潜在影响。

嵌入细胞的图上的时空学习